We want to solve the following equation.3x+3=exOne of the solutions is x≈−1.Find the other solution.Hint: Use a graphing calculator.Round your answer to the nearest tenth.x≈
Q. We want to solve the following equation.3x+3=exOne of the solutions is x≈−1.Find the other solution.Hint: Use a graphing calculator.Round your answer to the nearest tenth.x≈
Set Up Equation: First, we need to set up the equation that we are trying to solve: 3x+3=ex
Graph Functions: Since we are given a hint to use a graphing calculator, we will graph both sides of the equation as separate functions and look for their points of intersection.Function 1: y=3x+3Function 2: y=ex
Find Intersection: Using a graphing calculator, we plot both functions on the same set of axes. We already know that one intersection point is around x=−1. We are looking for the other point where the two graphs intersect.
Calculate Solution: After graphing, we find the other point of intersection by using the calculator's intersection feature or by visually inspecting the graph for the approximate value of x where the two functions meet.
Verify Solution: Assuming no mistakes were made in using the graphing calculator, we find the other solution for x and round it to the nearest tenth as instructed.Let's say the calculator gives us an intersection at x=1.5 (this is a hypothetical value for the purpose of this example).
Verify Solution: Assuming no mistakes were made in using the graphing calculator, we find the other solution for x and round it to the nearest tenth as instructed.Let's say the calculator gives us an intersection at x=1.5 (this is a hypothetical value for the purpose of this example).We check our solution by plugging it back into the original equation to see if both sides are approximately equal.3∗1.5+3?= e1.54.5+3?= e1.57.5?= e1.5
Verify Solution: Assuming no mistakes were made in using the graphing calculator, we find the other solution for x and round it to the nearest tenth as instructed.Let's say the calculator gives us an intersection at x=1.5 (this is a hypothetical value for the purpose of this example).We check our solution by plugging it back into the original equation to see if both sides are approximately equal.3∗1.5+3?= e1.54.5+3?= e1.57.5?= e1.5We use a calculator to find the numerical values of both sides to verify the solution.7.5≈2.74e1.5≈4.48Since these values are not approximately equal, we realize there has been a mistake in our calculation or in reading the graphing calculator's output.